Modified KS, AD, and C-vM tests for the Pareto distribution with unknown location and scale parameters

Author

Porter, James E., III ; Coleman, Joseph W. ; Moore, Albert H.

Author_Institution

Air Force Inst. of Technol., Wright-Patterson AFB, OH, USA

Volume

41

Issue

1

fYear

1992

fDate

3/1/1992 12:00:00 AM

Firstpage

112

Lastpage

117

Abstract

Standard goodness-of-fit tests based on the empirical CdF (Edf) require continuous underlying distributions with all parameters specified. Three modified Edf-type tests, the Kolmogorov-Smirnov (K-S), Anderson-Darling (A-D), and Cramer-von Mises (C-vM), are developed for the Pareto distribution with unknown parameters of location and scale and known shape parameter. The unknown parameters are estimated using best linear unbiased estimators. For each test, Monte Carlo techniques are used to generate critical values for sample sizes 5(5)30 and Pareto shape parameters 0.5(0.5)4.0. The powers of the modified tests are investigated under eight alterative distributions. In most cases, the powers of the modified K-S, A-D, C-vM tests are considerably higher than the chi-square test. Finally, a functional relationship is identified between the modified K-S and C-vM test statistics and the Pareto shape parameter. Powerful goodness-of-fit tests that supplement the best linear unbiased estimates are provided

Keywords

failure analysis; reliability theory; statistical analysis; Anderson-Darling test; Cramer-von Mises test; Edf-type tests; Kolmogorov test; Monte Carlo techniques; Pareto distribution; empirical distribution function; goodness-of-fit tests; linear unbiased estimates; location parameters; reliability; scale parameters; shape parameter; test statistics; unknown parameters; Monte Carlo methods; Parameter estimation; Pareto analysis; Power generation economics; Reliability theory; Shape; State estimation; Statistical analysis; Statistical distributions; Testing;

fLanguage

English

Journal_Title

Reliability, IEEE Transactions on

Publisher

ieee

ISSN

0018-9529

Type

jour

DOI

10.1109/24.126681

Filename

126681